In the 1990s, Microsoft Internet Explorer battled Netscape Navigator in the great Web-browser wars. In the 2000s, Google and Yahoo locked horns over Internet search — and we know how that turned out. Today, the latest high-stakes tech conflict is between Apple’s iPhone and Google’s Android mobile operating system for supremacy in the smart-phone market.

Each of these clashes defined an era of Internet history. Apple vs. Android is no different. Everyone agrees that the struggle for Internet advantage is shifting to the mobile realm, and iPhone and Android have surged to the front of the pack with diametrically opposed business models. Neither of these players will be vanquished anytime soon — these battles take years to play out — but the company that gains the upper hand will be best positioned to take advantage of the massive structural shift from desktop PCs to smart phones and tablets.

Apple and Google realize how huge the stakes are in this fight. Apple’s late CEO, Steve Jobs, revolutionized the mobile-phone market with the iPhone, and he was furious when Google launched Android because he was convinced it ripped off features from the iPhone. (In August, a San Jose, Calif., federal jury agreed.) Google, meanwhile, has poured millions of dollars into developing Android and billions more bolstering its intellectual-property position by buying Motorola Mobility for $12.5 billion.

This smart-phone showdown is important because Apple and Google are advancing radically different business models to the fight. This is bigger than just a commercial clash between two tech titans. It’s a war between two fundamentally different visions for the future of computing, described in simplistic terms as closed vs. open. Apple’s model is end-to-end control over the iPhone process, from hardware to software to the mobile applications that it must approve for sale in the App Store. Google’s model has been to distribute the Android system for free to the developer community at large and let a thousand flowers bloom.

Each company has been successful with its respective strategy: Apple makes $1 billion per month on iPhone sales, and the device is considered the gold standard for smart-phone design. Android, meanwhile, generates vastly less revenue per unit sold but has racked up massive market-share gains, growing to lead the global mobile OS space in just five years.

Speaking at an event in New York City earlier this week, Google executive chairman Eric Schmidt did not mince words describing the intensity of the showdown and what he characterized as its benefits to consumers. “The Android-Apple platform fight is the defining fight in the industry today,” Schmidt said at an event hosted by AllThingsD co-executive editors Kara Swisher and Walt Mossberg. “We’ve not seen platform fights at this scale,” he added, in comments cited by AllThingsD’s Liz Gannes. “The beneficiary is you guys [consumers]. Prices are dropping rapidly. That’s a wonderful value proposition.”

This battle may have “wonderful” consequences for consumers, but it hasn’t exactly been pleasant for the combatants. In addition to cutthroat competition in the marketplace, Apple has been slugging it out in courtrooms around the world over intellectual property with Google’s hardware partners. Apple’s global patent offensive against Samsung, HTC and other Google partners (including the search giant’s newly acquired Motorola Mobility division) is really a proxy fight against Android. In August, South Korea–based Samsung was hit with a $1.05 billion verdict after a federal jury concluded that it had infringed Apple’s iPhone patents.

To hear them tell it, top executives at both Apple and Google insist they would prefer not to engage in such expensive and drawn-out patent litigation, but at least in Apple’s case, the company feels it has no choice but to defend its flagship product. Last spring, Apple CEO Tim Cook declared that he’s “always hated litigation, and I continue to hate it,” but said it’s his job to protect Apple’s inventions. For his part, Schmidt told the New York audience that “these patent wars are death” and described the patent arms race as “bad for innovation. It eliminates choices.”

That view was backed up in the latest installment of the New York Times iEconomy series, which appeared earlier this week. “The marketplace for new ideas has been corrupted by software patents used as destructive weapons,” the story’s authors wrote, noting that last year, for the first time, Apple and Google spent more on patent litigation and intellectual property than on research and development, a striking fact that sharply illustrates how incentives have become skewed in the tech industry. Elsewhere in the article, a former Apple executive confirmed that in the case of the company’s 2010 lawsuit against HTC, a key Android partner, “Google was the enemy, the real target.”

Could Apple and Google finally be growing weary of the patent wars? There are the faintest glimmers of hope. Google CEO Larry Page and Apple’s Cook have been holding back-channel discussions “about a range of intellectual-property matters, including the ongoing mobile patent disputes between the companies,” Reuters reported six weeks ago. It’s encouraging to see these two tech titans talking, because consumers want to see these firms compete in the marketplace, not bicker in courtrooms. As the battle for smart-phone supremacy rages between Apple and Google, may the best products win — not the company with the best patent lawyers.